The point-slope form of a linear equation of a non-vertical line is given by:

Point-Slope Form of a Linear Equation

1 1y y m x x

1 1

is the slope of the line

is a point on the line

,

m

x y

Example 1: Write the point-slope form equation of the3

4.mline that contains the point (3, -5) and has slope

1 1y y m x x

Substitute values into the equation …

Slope: 1 1

3

4y y x x

3

4.m

Simplify:

35 3

4y x

Point:

3, 5

1 1,x y

3

45 3y x

1 1

3

4y y x x

Example 2: Write the slope-intercept equation of

2.

5m

the line that contains the point (- 2, 5) and has slope

First, substitute the given point and slope values into the point-slope equation.

1 1y y m x x

55 2

2y x

Simplify 55 2

2y x

Next, put in slope-intercept form, y mx b

55 2

2y x

55 2

2y x 2

22

Multiply each term by the common denominator …

2 10 5 2y x

Simplify and solve for y

2 10 5 2y x

2 10 5 10y x

2 5 20y x

510

2y x

Example 3: Write the slope-intercept equation of the line that contains the points (- 1, 8) and (4, - 2).

First, find the slope of the line using the given points.

m 2 1

2 1

y y

x x

2 8

4 1

10

5

2

Next, substitute either given point (let’s use (- 1, 8)) and the slope, - 2, into the point-slope equation.

Last, simplify and write in slope-intercept form.

8 2 1y x

8 2 1y x

8 2 2y x

2 6y x